Difference between revisions of "2005 AMC 10A Problems/Problem 15"
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==See Also== | ==See Also== |
Revision as of 22:58, 27 May 2013
Contents
Problem
How many positive cubes divide ?
Solution
Therefore, a perfect cube that divides must be in the form where , , , and are nonnegative multiples of that are less than or equal to , , and , respectively.
So:
( posibilities)
( posibilities)
( posibility)
( posibility)
So the number of perfect cubes that divide is
Solution 2
If you factor You get
There are 3 ways for the first factor of a cube: , , and . And the second ways are: , and .
Answer :